The first step of the offline stage (blue) represents an initialization of a training set (\(\mathbf {\mu }\) ) of parameters used to train the framework, of cardinality \(\mathrm {M}\) . Let \(\mathbb {P} \subset \mathbb {R}^P\) , \(P \in \mathbb {N}\) , be a compact set representing the range of variation of the parameters \(\mathbf {\mu } \in \mathbb {P}\) . For the sake of notation we denote by \(\mu _p\) , \(p = 1, \hdots , P\) , the \(p\) -th component of \(\mathbf {\mu }\) . To explore the parametric dependence of the phenomena, we define a discrete training set of \(\mathrm {M}\)  parameter instances. Each parameter instance in the training set will be indicated with the notation \(\mathbf {\mu }^{(i)}\) , for \(i = 1, \hdots , \mathrm {M}\) . Thus, the \(p\) -th component of the \(i\) -th parameter instance in the training set is denoted by \(\mu _p^{(i)}\)  in the following. The choice of the value of \(\mathrm {M}\) , as well as the sampling procedure from the range \(\mathbb {P}\) , is typically user- and problem-dependent. In this work, we use an equispaced distribution for the training set as done in [1]}. We note that adaptive sampling approaches could be employed and might result in a better model accuracy with a lower number of training instances [2]}, [3]}, [4]}.
